A Dialectica-Like Interpretation of a Linear MSO on Infinite Words
Résumé
We devise a variant of Dialectica interpretation of intuition-istic linear logic for LMSO, a linear logic-based version MSO over infinite words. LMSO was known to be correct and complete w.r.t. Church's synthesis , thanks to an automata-based realizability model. Invoking Büchi-Landweber Theorem and building on a complete axiomatization of MSO on infinite words, our interpretation provides us with a syntactic approach , without any further construction of automata on infinite words. Via Dialectica, as linear negation directly corresponds to switching players in games, we furthermore obtain a complete logic: either a closed formula or its linear negation is provable. This completely axiomatizes the theory the realizability model of LMSO. Besides, this shows that in principle, one can solve Church's synthesis for a given ∀∃-formula by only looking for proofs of either that formula or its linear negation.
Domaines
Logique en informatique [cs.LO]Origine | Fichiers produits par l'(les) auteur(s) |
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